随机滞后微分方程的有界性

Boundedness of stochastic retarded differential equations

研究了随机滞后微分方程的一致有界和一致最终有界.利用Lyapunov函数和Razumikhin技巧,得到了一些关于随机滞后微分方程有界性新的Razumikhin定理,同时,证明随机滞后微分方程解的存在性,推广了相关的文献.最后,给出例子证实定理的有效性.

In this paper,the uniform boundedness and uniform ultimate boundedness of the stochastic retarded differential equations is investigated.The new Razumikhin theorems of boundedness about these systems are obtained by using the Lyapunove functions and Razumikhin technique.It should be noted that the boundedness criteria prove the global existence of solutions as well as boundedness,thus the available results in references are improved.Finally,an example is illustrated to verify the theorems.